Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-04
Nucl.Phys.B775:95-119,2007
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, 3 figures
Scientific paper
10.1016/j.nuclphysb.2007.04.004
We study the solutions of the Euclidean-signature Einstein equations (gravitational instantons) whose line-element takes the Kerr-bolt form, characterized by three real parameters: a size, a NUT charge, and a spin rate. The exclusion of singularities eliminates most combinations of these parameters, leaving only separated solution-manifolds between which continuous transitions are impossible (The angular velocity divided by the temperature is forced to be a rational multiple of $2\pi$). This ``quantization'' prevents the free variations presupposed by an equation like $T dS=dM + \Omega dJ$, and thereby renders the first law true, false, meaningless, or tautological, depending on how one approaches it.
Ghezelbash Amir Masoud
Mann Robert B.
Sorkin Rafael D.
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